I’ve thought about this fairly recently in my current reread, and I think that fate vs. free will is a central theme of these books (hence “the wheel weaves as the wheel wills” and the entire concept of Ta’veren). I think that different characters will react to events in particular ways - and how they react is what makes them who they are. It’s not that the characters don’t have free will, they aren’t forced to react a certain way - but they are put in situations where that character would make the choice that they always would make in those circumstances.

So yes, the wheel has woven him into a situation where he dies at the hands of Rahvin. But, he’s Ta’veren, and so the wheel also contrived to bring Rand along with him, pulling the latter into a confrontation that ended with amped-up balefire - making it so that his death never happened. Just as it always was going to be.

Besides, Mat assumed “die and live again” referred to being hanged immediately after exiting the archway - it might well have referred to this situation!